Public broadcaster France Televisions will team up with private channels TF1 and M6 for the new site, which has been named Salto.
"Through Salto the France Televisions, M6 and TF1 groups intend to offer an ambitious response to the new expectations of the public," the channels said in a joint statement.
Like Netflix and Amazon, Salto will offer TV programmes and films under a monthly subscription which can be cancelled at any time.
The channels said the new platform would have "unparalleled variety", offering both live programming and catch-up TV shows that can be watched at any time.
TF1 and France Televisions account for 75 percent of TV production in France, and the three companies said they were open to other channels joining the project.
They have yet to say when the new service will launch and how much it will cost, but a source close to the talks said it will likely be priced at five euros ($5.80) a month.
Salto will also need to work out "the best way of working with the existing free platforms" run by TF1, France Televisions and M6, the statement said.
Channels in other countries have already teamed up to form similar joint streaming sites, such as Hulu in the United States, formed by Walt Disney, 21st Century Fox, Comcast and AT&T.
French channels are acutely aware of the draw of US platforms such as Netflix, which has attracted 3.5 million subscribers in four years, according to the Liberation newspaper.